Brittle fracture in materials with random defects

Hassold, Gregory N.; Srolovitz, David J.

doi:10.1103/physrevb.39.9273

Cited by 91 publications

(48 citation statements)

References 18 publications

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“…With respect to modeling material fracture, the simplest and one of the most popular forms of interaction is through central force ͑or axial͒ springs. [4][5][6] A more general form of interaction is provided by the Born model, 7 which includes both axial and transverse stiffnesses, although this model in not rotationally invariant. With the introduction of rotational degrees of freedom at the element nodes, bond-bending, 8 granular, and Euler-Bernoulli beam 9,10 models overcome the deficiency of the Born model and allow for a more general interaction between the neighboring sites that, in the limit, relate to a gradient continuum, such as Mindlin-Toupin or Cosserat continua.…”

Section: Introductionmentioning

confidence: 99%

Irregular lattice model for quasistatic crack propagation

2005

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An irregular lattice model is proposed for simulating quasistatic fracture in softening materials. Lattice elements are defined on the edges of a Delaunay tessellation of the medium. The dual ͑Voronoi͒ tessellation is used to scale the elemental stiffness terms in a manner that renders the lattice elastically homogeneous. This property enables the accurate modeling of heterogeneity, as demonstrated through the elastic stress analyses of fiber composites. A cohesive description of fracture is used to model crack initiation and propagation. Numerical simulations, which demonstrate energy-conserving and grid-insensitive descriptions of cracking, are presented. The model provides a framework for the failure analysis of quasibrittle materials and fiber-reinforced brittle-matrix composites.

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Section: Introductionmentioning

confidence: 99%

Irregular lattice model for quasistatic crack propagation

2005

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“…The deformation state of this lattice is fully identified by the value of the lattice angle a and the point-to-point strain 1, so that the lattice strains e x , e y along the principal directions are obtained by a simple projection. Following other researchers [40,41], we describe the lattice elasticity by means of the Born model. Here, each material point is connected only to its nearest neighbours by two kinds of springs: a longitudinal spring K l and a transverse one K t .…”

Section: Born Lattice Modelmentioning

confidence: 99%

Pressurized honeycombs as soft-actuators: a theoretical study

Guiducci

Fratzl

Bréchet

et al. 2014

J. R. Soc. Interface.

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The seed capsule of Delosperma nakurense is a remarkable example of a natural hygromorph, which unfolds its protecting valves upon wetting to expose its seeds. The beautiful mechanism responsible for this motion is generated by a specialized organ based on an anisotropic cellular tissue filled with a highly swelling material. Inspired by this system, we study the mechanics of a diamond honeycomb internally pressurized by a fluid phase. Numerical homogenization by means of iterative finite-element (FE) simulations is adapted to the case of cellular materials filled with a variable pressure fluid phase. Like its biological counterpart, it is shown that the material architecture controls and guides the otherwise unspecific isotropic expansion of the fluid. Deformations up to twice the original dimensions can be achieved by simply setting the value of input pressure. In turn, these deformations cause a marked change of the honeycomb geometry and hence promote a stiffening of the material along the weak direction. To understand the mechanism further, we also developed a micromechanical model based on the Born model for crystal elasticity to find an explicit relation between honeycomb geometry, swelling eigenstrains and elastic properties. The micromechanical model is in good qualitative agreement with the FE simulations. Moreover, we also provide the force-stroke characteristics of a soft actuator based on the pressurized anisotropic honeycomb and show how the internal pressure has a nonlinear effect which can result in negative values of the in-plane Poisson's ratio. As nature shows in the case of the D. nakurense seed capsule, cellular materials can be used not only as low-weight structural materials, but also as simple but convenient actuating materials.

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“…Such restriction is not suitable for many materials and it can be overcome by introducing non-central force interactions (shear springs) between particles. Hassold and Srolovitz [16] proposed a method to modify the Poisson's ratio by introducing a harmonic potential for rotation of bonds from their initial orientation. Here bonds denote the connecting elements between particles.…”

Section: Introductionmentioning

confidence: 99%

“…Here the discrete units are merely lattice sites (nodes). This type of models can be further classified into lattice spring [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] and lattice beam [23][24][25][26] models according to the number of degrees of freedom per node and the mechanical properties of connecting elements. In a lattice three-dimensional cases and 0.33 for two-dimensional cases.…”

Section: Introductionmentioning

confidence: 99%

A MLS-Based Lattice Spring Model for Simulating Elasticity of Materials

Guo-jie

Fang

Zhao

2012

Int. J. Comput. Methods

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A MLS-based lattice spring model is presented for numerical modeling of elasticity of materials. In the model, shear springs between particles are introduced in addition to normal springs. However, the unknowns contain only particle displacements but no particle rotations. The novelty of the model lies in that the deformations of shear springs are computed by using the local strain obtained by the moving least squares (MLS) approximation rather than using the particle displacements directly. By doing so, the proposed lattice spring model can represent the diversity of Poisson's ratio without violating the requirement of rotational invariance. Relationships between micro spring parameters and macro material constants are derived from the Cauchy-born rules and the hyperelastic theory. Numerical examples show that the proposed model is able to reproduce elastic solutions obtained by finite element methods for problems without fractures. Therefore, it is capable of simulating solid materials which are initially continuous, but eventually fracture when critical stress and/or displacement levels are reached. A demonstrating example is presented.

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Brittle fracture in materials with random defects

Cited by 91 publications

References 18 publications

Irregular lattice model for quasistatic crack propagation

Irregular lattice model for quasistatic crack propagation

Pressurized honeycombs as soft-actuators: a theoretical study

A MLS-Based Lattice Spring Model for Simulating Elasticity of Materials

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